Wilkinson Microwave Anisotropy Probe

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Product Name
Cosmological Parameters


Analysis of the WMAP data involved the computation of cosmological parameters assuming a variety of models and including a variety of datasets in addition to the WMAP dataset. The various model/dataset combinations that were tested are displayed in a matrix; the combinations that were analyzed have links in the corresponding cells to individual display pages that show the cosmological parameters computed using that combination of model and dataset. A printable version of each list of parameters is made available as a Postscript file through a link its corresponding the individual display page.

Mnemonics are used to identify the models and datasets in the table and the individual model/dataset displays. The following table translate the mnemonics:

Mnemonic Description Mnemonic Description
LCDM ΛCDM YHE ΛCDM with a variable primordial Helium fraction
WCDM Dark energy equation of state (w) allowed
to vary.
ISO1 Anticorrelated CDM isocurvature.
OLCDM ΩK allowed to vary. ISO2 Uncorrelated CDM isocurvature.
OWCDM ΩK and w allowed to vary. MNU Massive neutrinos.
WACDM Time-dependent dark energy equation of state, given by
w(a) = w0 + wa (1-a)
NREL Number of relativistic species.
LENS Turn on lensing when computing
CMB spectrum.
NREL > 3 Number of relativistic species greater than three.
SZ Floating amplitude for SZ spectrum. RUN Running spectral index.
DELZ ΛCDM with a variable width reionization
epoch, Δz
TENS Tensor modes.
Mnemonic Description
WMAP7 WMAP seven year data set
WMAP7.1 WMAP seven year data set run with version 4.1 of the WMAP likelihood software and version 1.5 of RECFAST1.
BAO Baryonic Acoustic Oscillations (Percival, et.al., 2009)
CMB Small-scale CMB observations from ACBAR and QUAD
LRG Sloan Luminous Red Galaxy Sample (Reid, et.al., 2009)
H0 Hubble constant (Riess, et.al., 2009)
SNCONST Type Ia supernovae from the Constitution dataset (Hicken et.al., 2009, 0901.4804)
SNSALT Type Ia supernovae from the extended SDSS dataset (Kessler et.al., 2009), processed with SALT
TDEL Time delay measurements (Suyu, et.al., 2009)

1 RECFAST is the code included in the Code for Anisotropies in the Microwave Background (CAMB) that calculates the fractional ionization of the light elements in the universe for a range of redshifts around z=1000 for the purpose of determining the cosmic microwave background power spectra.

As mentioned previously, each model/dataset combination has an individual display page that shows the WMAP measurements of the cosmological parameters, with a link to a Postscript file showing the same parameters. These display pages also contain links to files containing WMAP's best fit Cl's, best fit matter power spectra, and Monte Carlo Markov Chains. The Markov Chain are supplied in a compressed tarball that contains a README file describing the contents. The spectra files contain:

  • Best fit Cl scalar files contain four columns: l, TT, EE, and TE. The tensor and total files contain five columns: l, TT, EE, BB, and TE. The Cl columns are scaled: T02 l (l + 1) Cl / 2&pi in µK2;
  • Best fit matter power spectra files contain two columns. The first column is k/h in units of Mpc-1. The second column is the linear matter power spectrum P(k), defined such that the variance is: σ2 = (2π)-3 ∫d3k P(k)

Some of the Markov Chains are flagged as "post-processed". These chains have been constructed from chains originally run with a different data combination. Importance sampling (Lewis & Bridle, 2002) was used to reweight the original chain for the new dataset. The new distribution is checked against the original chain to determine if the statistics can be trusted. Some of the contents of these chains differ from normal chains:

  • Weights:
    • The usual 'weight' file appears. It has non-integer entries, as the original weights have been scaled to correspond to the new data set.
    • An additional file 'weight_old' appears. This corresponds to the weight file of the original data set, and is not required for analysis of this chain.
  • Likelihoods:
    • The 'lnlike' file contains the -log likelihood of the ORIGINAL chain.
    • The 'del_lnlike' file contains the change in -log likelihood from the reweighting step.

To find the -log likelihood of this chain, you should therefore use total lnlike = 'lnlike' + 'delta_lnlike'

Additional Information

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Goddard Space Flight Center, National Aeronautics and Space Administration
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LAMBDA Director: Dr. Eric R. Switzer
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